(FORTUNE Magazine) – ROBERT B. HORTON, chairman of British Petroleum, may have the toughest job in the oil business. With revenues last year of $50 billion, BP is the fourth- largest private oil company in the world after Exxon, Royal Dutch Shell, and Mobil. It holds vast reserves, about five billion barrels, and when Iraq invaded Kuwait the market value of those barrels rose by $100 billion. So what's the problem? Haunting Horton is the fact that over 80% of BP's oil production is concentrated in two giant but aging fields, Prudhoe Bay in Alaska and the Forties field in the North Sea. Half a world apart, these two bonanzas were both discovered and developed in the late 1960s and 1970s and reached maturity at almost the same time in the late 1980s. Now they are past their prime, and production from their wells is dropping nearly 10% a year. The effect on the bottom line is more pronounced: Alaska and the North Sea generate roughly 42% of the company's operating profits while accounting for only 16% of its revenues. It's a case of too many eggs in one -- make that two -- barrels. Finding and exploiting opportunities to compensate for declining production will require the sort of flexible, fast-moving organization that BP never was. That's Horton's other problem. He is at the top of a multi-tiered, old, sclerotic bureaucracy that stifles speed and imagination. Born the son of a timber merchant in a land with few forests, Horton, 51, is not daunted by the challenge of thriving amid dwindling resources. Even before he became chairman in March, he began to implement a sweeping strategy to rejuvenate BP by combining wildcat exploration on the globe's few remaining oil frontiers with a thorough dismantling of the company's notorious bureaucracy -- a cultural revolution intended to shake BP to bedrock. It has already begun, and with a vengeance: Corporate staff, numbering 2,500 about a year ago, is now 380 and still falling. Says Bruce Lazier, an analyst with San Jacinto Securities in Dallas: ''It's hard to believe this is the same old sleepy BP.'' Meeting the challenges will require formidable leadership talent, which Horton appears to have plenty of. In the 1980s he was the company's top trouble-shooter. First he hacked the refining and chemical division into profitability, earning the moniker Horton the Hatchet. In 1986 he went to Cleveland to restructure Standard Oil of Ohio, cutting middle management and overseeing BP's acquisition of the 45% of Sohio it didn't already own. (He earned $2 million a year in Cleveland but makes $800,000 now.) While there, he worked closely with a shrewd financial adviser named John Browne, and the two became known as Batman and Robin -- Horton being big and burly, Browne small and quick. Browne now heads BP's exploration and production division, and some observers believe he will succeed Horton at the top. Horton has a knack for carrying out the unpleasantness of restructuring while stirring up a minimum of resentment. He seems to be always moving, always shaking hands, never hiding in the executive suite. Remembers an executive who watched him work in Cleveland: ''He cut Sohio's contributions to charity by almost $4 million but also joined the boards of both the Cleveland Orchestra and the Rock 'n' Roll Hall of Fame, which was struggling to get started.'' It seems fitting that a CEO who would support the Rock 'n' Roll Hall of Fame would devise BP's unusual frontier strategy. Large oil companies generally spend most of their exploration budgets looking for new reservoirs in regions where oil has already been discovered and developed. That's partly because the number of frontiers is dwindling, but caution also plays a role. One of every three or four wells drilled in mature regions typically strikes commercial quantities of crude, while one in ten is the usual success ratio in virgin territory. Unfortunately, as each region is developed, new discoveries become progressively smaller and less profitable. Says Horton: ''Eventually exploration in mature hydrocarbon provinces becomes an excellent way of wasting money.'' Horton's arithmetic led him to a different plan. He figures that within five years of the first discovery in a new basin, all of the big reservoirs -- called ''elephants'' and containing 100 million barrels or more -- have usually been discovered. These yield the highest profits, as BP knows: Prudhoe Bay and the Forties field were such discoveries. The trick is getting into frontiers early. By BP's estimate, 1,350 sedimentary basins on earth are capable of holding significant quantities of oil and gas, and about 1,000 of these have been opened up. The rest have remained undrilled because they were in countries closed to exploration (like the Soviet Union or Vietnam) or in inaccessible environments, such as ocean waters deeper than 2,000 feet or so. But now, governments that were hostile to foreign explorers are turning friendly, a trend likely to accelerate in the wake of Iraq's invasion of Kuwait. And the advance of technology will soon bring seabed regions as deep as 6,000 feet within reach. Horton is going elephant hunting in these new regions. He is keeping most of his targets secret but acknowledges that BP is looking in Vietnam, Papua New Guinea, Ethiopia, Angola, and the Philippines. To help Browne's explorers zero in on drilling prospects, the company has developed airplane-mounted laser sensors that can detect microscopically thin oil slicks on the surface of the ocean, the result of seepage from oil deposits below the seabed. Browne has sent the three laser planes to prowl most of the globe's outer continental shelves in search of the telltale signs of another Prudhoe Bay. This year BP will spend up to half its $1 billion exploration budget on the frontiers. Bernard Picchi, a managing director of Salomon Brothers, estimates that most big oil companies spend about 10% of their budgets on frontier, or wildcat, exploration. If the frontier strategy starts to yield new discoveries, Horton figures it will be at least 1995 before they can be developed. In the meantime, BP will press to increase natural gas production, particularly in the North Sea, for use in Europe. Browne says the company's natural gas output, which has already begun climbing (see chart), will increase from 13% of BP's total production to 20% by 1995. Horton's second goal is to shatter the company's bureaucracy and replace it with teams that will, he hopes, respond quickly to changing conditions and make the company a desirable place to work. At times he sounds almost Woodstockian: ''When I returned from Cleveland to London, I spent six months in deep culture shock because until I had been away for a couple of years, I hadn't realized how deeply embedded the bureaucracy, the distrust, the second- guessing, had become. We want a more flexible organization that works on trust and openness and teamwork rather than on hierarchy. If the Eighties were a time of change, the Nineties will be a decade of surprise.'' To help him bust up the bureaucratic concrete, Horton last fall appointed a team (don't you dare call it a committee) of seven young executives in their 30s and early 40s to redesign the way the company works. Their plan begins by reshaping headquarters. Horton expects it will take two to five years to penetrate to all of BP's far-flung extremities. Project 1990, as it is known, looks like this. Payroll cuts and reassignments are accomplishing most of the shrinkage in corporate staff. The diminished group will move from a giant and sooty modern office tower into a gracious old building that was the company's headquarters in the 1920s. Abolished are 80 standing committees, and six of the 11 managerial layers that used to stand between Horton and his first-line supervisors. To empower people down through the organization, Horton has increased by 2 1/2 times on average the amount of money that managers can spend without authorization. The total increase in discretionary funds: $150 million. Spending authorizations that typically required 12 or 13 signatures now need two or three. Many have taken such measures before, but it is a trademark of Robert Horton that he tries to go one step beyond. The corporate staff, for instance, is being organized entirely into teams, each reporting directly to Horton, chief operating officer David Simon, or one of the heads of the four division: exploration and production, refining and marketing, chemicals, and nutrition (mainly animal feed). Information services, a huge central facility in many corporations, has been broken up and put entirely in the hands of the four divisions. HORTON LIKES to do what he calls personal things -- such as firing and promoting people -- face to face. That isn't always easy in a worldwide organization, so near his office he has installed a teleconferencing room, which he uses frequently, and he has made BP one of the largest users of that medium. In addition, many managers as far apart as Anchorage, Cleveland, and London are being connected with computerized messaging. Horton's campaign for a new corporate culture -- ''openness will make us the best,'' he says -- is greeted with some skepticism. Chief operating officer Simon, who was Horton's main rival for the chairmanship, says, ''Really, we've always had teamwork around here.'' But a younger woman executive in the ranks says, ''People here are not as cynical as I expected. They're saying, 'Okay, I'll give it a try.' '' That's about all the new boss can ask. The next question is whether the new approach can produce new barrels of reserves.

CHART: NOT AVAILABLE CREDIT: SOURCES: SALOMON BROTHERS, BRITISH PETROLEUM CO. CAPTION: BP'S CRUDE DILEMMA

CHART: NOT AVAILABLE CREDIT: NO CREDIT CAPTION: INVESTOR'S SNAPSHOT BRITISH PETROLEUM